ADVERTISING, INNOVATION
AND ECONOMIC GROWTH
Laurent Cavenaile and Pau Roldan
Documentos de Trabajo
N.º 1902
ADVERTISING, INNOVATION AND ECONOMIC GROWTH (*)
Laurent Cavenaile (**)
UNIVERSITY OF TORONTO
Pau Roldan (***)
BANCO DE ESPAÑA
Documentos de Trabajo. N.º 1902 2019
(*) We are indebted to Jess Benhabib for his invaluable advice and support, and to Gian Luca Clementi, Boyan Jovanovic, and Edouard Schaal for continued discussions and suggestions. For helpful comments, we thank Salomé Baslandze, Alberto Bisin, Jaroslav Borovička, Murat Celik, Diego Daruich, Tülin Erdem, Jeremy Greenwood, Seher Gupta, Siddharth Hari, Masakazu Ishihara, Olga Itenberg, Julian Kozlowski, Pedro Mendi, Simon Mongey, Ilari Paasivirta, Michael Peters, Xavier Ragot, Tom Schmitz and Gianluca Violante. We also received valuable feedback from seminar participants at Aarhus University, Atlanta Fed, Bank of Canada, Banco de España, KU Leuven, New York University, Rotman School of Management, Royal Holloway University of London, Southern Methodist University, Temple University, University of Melbourne, University of Montreal, UQAM, Western University, and from participants at the EEA Congress (Cologne), the Midwest Macroeconomics Meetings (Madison), the North American Summer Meeting of the Econometric Society (Philadelphia), SED (Toulouse), XIII REDg (Madrid), and the XXXI Jornadas de Economía Industrial (Palma de Mallorca). Any remaining errors are our own. The views expressed in this paper are those of the authors and do not necessarily coincide with those of the Banco de España or the Eurosystem.
(**) University of Toronto, 105 Saint George Street, Toronto, Ontario, M5S 3E6, Canada. Email: laurent.cavenaile@ utoronto.ca
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Abstract
This paper analyzes the implications of advertising for fi rm dynamics and economic growth through its interaction with R&D investment at the fi rm level. We develop a model of endogenous growth with fi rm heterogeneity that incorporates advertising decisions. We calibrate the model to match several empirical regularities across fi rm size using U.S. data. Through a novel interaction between R&D and advertising, our model provides microfoundations for the empirically observed negative relationship between both fi rm R&D intensity and growth, and
fi rm size. Our model predicts substitutability between R&D and advertising at the fi rm level. Lower advertising costs are associated with lower R&D investment and slower economic growth. We provide empirical evidence supporting substitution between R&D and advertising using exogenous changes in the tax treatment of R&D expenditures across U.S. states. Finally, we fi nd that R&D subsidies are more effective under an economy that includes advertising relative to one with no advertising.
Keywords: endogenous growth, advertising, innovation, research and development, fi rm dynamics, policy.
Resumen
Este artículo analiza las consecuencias que los gastos publicitarios tienen para la dinámica empresarial y el crecimiento económico, a través de la interacción entre la publicidad y los gastos en investigación y desarrollo (I+D) en las empresas. Presentamos un modelo de crecimiento económico endógeno con heterogeneidad entre empresas que incorpora decisiones sobre gastos en publicidad. Calibramos el modelo usando microdatos para Estados Unidos, con el fi n de estudiar patrones empíricos existentes entre empresas de distinto tamaño. Mediante la interacción entre publicidad e I+D, nuestro modelo propone una nueva explicación para la correlación negativa observada en los datos entre la intensidad innovadora y el tamaño empresarial. Nuestro modelo predice que los gastos en publicidad y en I+D son sustitutos en las empresas. Reducir costes publicitarios conlleva una reducción de inversión en I+D, así como una ralentización del crecimiento económico. A continuación, presentamos la evidencia empírica que demuestra la existencia de dicha sustitución mediante el uso de variación regional exógena en la política impositiva estadounidense referente a gastos en I+D. Finalmente, demostramos que los subsidios a la innovación son más efectivos en una economía que permita a las empresas publicitar sus productos respecto a una en la que la publicidad no esté permitida.
Palabras clave:crecimiento endógeno, publicidad, innovación, investigación y desarrollo, dinámicas empresariales, políticas públicas.
1
Introduction
Since the seminal contributions of Romer (1990), Grossman and Helpman (1991) and
Aghion and Howitt (1992), the economic literature has widely emphasized the role of
in-novation in the process of economic growth. Research and Development (R&D) introduces
goods of higher quality and enhanced production technologies which raise living standards.
From a firm’s perspective, innovation is used strategically to increase profits: by performing
R&D, firms can increase their market share by selling higher quality goods and diverting
de-mand from lower-quality products. Yet, while this process and its implications for economic
growth are relatively well understood in the literature, there exists a variety of other tools
that firms may use to direct demand towards their products.1 One non-negligible example
is advertising.
By advertising their goods, firms can alter consumer preferences and ultimately increase
product-specific profits. This suggests that innovation and advertising may be substitutable
tools in firms’ quest for higher profits. Additionally, advertising and innovation investments
may also be complementary, as the former type of investment raises the return to innovation
by increasing market shares of new products. In either view, advertising decisions are not
neutral in terms of global economic growth. In fact, both these types of investment represent
sizable expenditures in aggregate terms. Over the 1980-2013 period in the U.S., the share
of R&D expenditures over GDP fluctuated between 2.27% and 2.82%.2 Over the same time
period, firms in the U.S. spent on average around 2.2% of GDP on advertising each year.3
Yet, the growth literature is relatively silent on the potential interaction between R&D and
advertising expenditures and its potential impact on firm growth, firm dynamics and long
run economic development.
In this paper, we ask how advertising affects R&D investment decisions at the firm level
and study the implications for economic growth and firm dynamics. We build a flexible model
that captures different dimensions of complementarity and substitutability between R&D and
advertising. Our calibrated model shows that a decrease in the relative cost of advertising
can have significant detrimental effects on long run economic growth as the substitution
effect dominates. We provide supportive empirical evidence for substitution between R&D
and advertising using U.S. firm-level data. We also find that the interaction between R&D
and advertising can generate some observed empirical regularities related to firm dynamics,
such as decreasing firm growth rates with firm size (a deviation from the so-called Gibrat’s
law) as well as decreasing R&D intensity with firm size.
1A recent trend in the macroeconomic literature has started investigating several types of intangible investment
and their potential implications for the overall economy. See for instance, McGrattan and Prescott (2014), McGrat-tan (2017), Gourio and Rudanko (2014a), Hall (2014), Molinari and Turino (2015), Gourio and Rudanko (2014b), Arkolakis (2010, 2016) and Atkeson and Kehoe (2005).
2Source: OECD data, available at http://data.oecd.org/rd/gross-domestic-spending-on-r-d.htm.
3Source: Coen Structured Advertising Expenditure Dataset, extracted from the McCann Erikson advertising
agency (available at http://www.purplemotes.net/2008/09/14/us-advertising-expenditure-data/).
Theoretically, we build on the Akcigit and Kerr (2018) model of endogenous growth
through R&D, which we extend to incorporate explicit advertising decisions. Firms are
quality grows on a ladder through innovation arising from investment in R&D, which can take
two forms in our model. Through internal R&D, firms can increase the quality of their own
goods. External R&D, on the other hand, enables incumbent firms and potential entrants
to improve on the quality of a good that they do not own and displace the former producer
through creative destruction. Besides R&D, firms can use advertising to expand their
mar-ket shares and profit. Firms use advertising to influence the perception that consumers have
of their goods, thereby altering preferences and ultimately shifting demand toward those
products.
We calibrate the model via indirect inference using both aggregate and micro-level data.
Our model is calibrated to match four empirical facts related to firm dynamics and investment
across firm size. Figure 1 shows these four facts. The upper-left panel displays the average
growth rate of publicly-listed firms in the U.S., by size quintiles.4 Growth rates are higher
for smaller firms and are consistently decreasing with firm size. The upper-right panel shows
that small firms also tend to be relatively more R&D intensive. This suggests that smaller
firms experience higher growth through relatively higher R&D investments, a conclusion
that has sometimes been interpreted in the existing literature as evidence of differences in
R&D technology across firm size. This can have important implications in terms of policy
recommendations (e.g. Akcigit (2009), Acemoglu et al. (2018) or Akcigit and Kerr (2018)).
If small firms are more efficient at innovating, R&D subsidies targeted at small firms may
be optimal. An important question is then to understand the source of the deviation from
constant R&D intensity across firm size. In this context, our paper provides microfoundations
for this deviation. We show that the observation that R&D intensity diminishes with firm size
can arise as the result of the optimal allocation of resources between R&D and advertising
at the firm level.
Our calibration is also disciplined by two new facts about advertising. First, we find a
negative relationship between advertising intensity (i.e., advertising expenditures normalized
by size) and firm size, which can be observed in the lower-left panel of Figure 1. Second, we
find that larger firms rely relatively more on advertising compared to R&D, as the ratio of
R&D to advertising expenditures decreases with firm size (lower-right panel in Figure 1).
Our calibration delivers two main implications regarding the interaction between R&D
and advertising. First, our results show the existence of a substitution effect between R&D
and advertising at the firm level. A decrease in the cost of advertising leads to an increase
in the entry rate and in creative destruction. This, in turn, decreases the incentive for
incumbent firms to invest in R&D and shifts the firm size distribution to the left (larger
4Data include U.S. listed companies performing R&D and advertising between 1980 and 2015 from the
Compu-stat database. More details on the sample selection in Section 3.
mass of small firms). Overall, investment in R&D decreases which leads to a decrease in
economic growth. In particular, we predict that the growth rate of the economy would be
0.64 percentage points higher if advertising is shut down from the model. Second, we find
that the interaction between R&D and advertising can quantitatively deliver the four facts
reported in Figure 1, which suggests that the deviation from constant R&D intensity across
firm size should not necessarily be interpreted as evidence for differences in R&D efficiency
The main new mechanisms in our model are based on well-established empirical
obser-vations from the marketing literature. Crucially, there is ample evidence in this literature
that larger firms have a cost advantage in terms of advertising compared to firms with fewer
products. One reason for this size advantage comes from a spillover effect through
differ-ent goods under the same brand name (umbrella branding). By advertising one product, a
firm can influence not only the perception of the quality of the advertised good but also of
other goods sharing the same brand name. The existence of this spillover effect alters firms’
dynamic incentives to engage in R&D. As smaller firms gain relatively more in terms of
ad-vertising spillover from acquiring an additional product, they optimally choose to perform
relatively more (external) R&D in order to expand into new product markets. As a result,
these firms grow relatively faster than large ones.
To validate our estimation, we show that the calibrated model also matches several
un-targeted moments among which the observed decrease in the variance of firm growth, as
well as of R&D and advertising intensity, with firm size. Moreover, using exogenous vari-Notes: Firms are ranked in size quintiles according to their normalized level of sales (sales
as a ratio of average sales in the same year). R&D and advertising intensities are measured as the ratio of total R&D and advertising expenditures to total sales within each group.
1 2 3 4 5
0 0.2 0.4
Fact #1: Sales growth
1 2 3 4 5
0 0.1 0.2
Fact #2: R&D / Sales
1 2 3 4 5
0 0.02 0.04 0.06
Size Quintile Fact #3: ADV / Sales
1 2 3 4 5
0 2 4
Size Quintile Fact #4: R&D / ADV
Q1 − Q5: 72.6% decrease Q1 − Q5:
83.0% decrease
Q1 − Q5: 58.5% decrease Q1 − Q5:
34.0% decrease
Figure 1: Firm growth, R&D intensity, advertising intensity, and R&D-advertising ratio, across firm size quintiles.
ation in the cost of R&D arising from changes in the tax treatment of R&D expenditures
across U.S. states and over time, we provide empirical evidence supporting the substitution
between R&D and advertising which is at the core of the predictions of our calibrated model.
Interestingly, we also find that R&D is complementary to other types of expenditures.
In the last part of the paper, we study the policy implications of our model. First,
we show that taxes on advertising, while desirable from the angle of growth, might have a
relatively small impact because (i) the elasticity of advertising to sales is low, and (ii) the tax
deters the entry of small and innovative firms. Second, we show that identifying the source
subsidies are more effective at promoting economic growth if the deviation from constant
R&D intensity comes from the interaction between R&D and advertising rather than from
technological differences in terms of R&D efficiency across firm size (for example, the increase
in growth is 0.12 percentage point higher in the former case for a 50% subsidy). We further
show that the model with advertising performs better in terms of matching moments related
to firm growth and R&D intensity across firm size.
The rest of the paper is organized as follows. Section 2 presents a comprehensive review
of the literature with a special focus on endogenous growth, firm dynamics and the
mar-keting literature used to motivate our advertising modeling approach. Section 3 presents
key empirical facts related to Gibrat’s law, R&D and advertising intensity at the firm level,
as well as the relative use of R&D and advertising across firm size. We then describe the
model in Section 4. Section 5 presents the calibration and shows that our novel advertising
mechanism is able to quantitatively replicate the main empirical regularities described in
Section 3. We also utilize the calibrated model to ask how advertising affects the firm size
distribution, firm entry rates and economic growth. In Section 6 we present a set of
valida-tion exercises, including the model’s performance in terms of untargeted moments (in Secvalida-tion
6.1), and empirical evidence supporting the main mechanism at work behind the calibrated
model (in Section 6.2). Section 7 investigates policy implications regarding advertising taxes
and R&D subsidies. We also compare the quantitative performance of our baseline model
with a calibration without advertising in matching moments. Section 8 concludes. The
Ap-pendix includes proofs of all the results, model extensions mentioned in the main text, and
additional tables and figures.
2
Related Literature
Our work is related to several strands of the literature. First and foremost, we build upon
models of endogenous firm growth through product innovation. This area was pioneered
by Klette and Kortum (2004), who built a stylized version of the Schumpeterian
creative-destruction models of Grossman and Helpman (1991) and Aghion and Howitt (1992) into a
model of multi-product firm dynamics. Their work is able to exhibit several patterns that are consistent with empirical finding coming from micro-level data, especially regarding the
right-skewness in the firm size distribution, the persistence in firms’ R&D investments, and
the volatility of innovation in the cross-section of firms.5
However, by assuming that firm productivity scales perfectly with size, this framework
fails to explain why firms of different sizes may grow at different rates. Indeed, empirical
studies have argued that there exist deviations from Gibrat’s law among innovative firms:
small establishments grow faster than large ones, and net exit rates are a decreasing function
of size.6
5The applied work by Lentz and Mortensen (2008) further unveiled the predictive power of the Klette and
Kortum (2004) model by putting it to a rigorous empirical test.
6See Hall (1987), Sutton (1997), Caves (1998), and Geroski (1998). For a survey of this empirical literature, see
( )
7Cohen and Klepper (1996) show that small innovating firms generate more innovations per dollar spent in
R&D, and Akcigit and Kerr (2018) show that small firms spend more in R&D per dollar of sales.
8For instance, weak scalability in the innovation technology (Akcigit and Kerr (2018)); larger step sizes of
technical advance for small firms (Acemoglu and Cao (2015)); or lower productive capacity as a highly absorbing state (Acemogluet al.(2018)).
One contributor to such phenomenon is that smaller firms tend to be more
innovation-intensive.7 Accordingly, a wave of second-generation models of innovation-driven firm growth
has emerged (Acemogluet al.(2018), Acemoglu and Cao (2015) and Akcigit and Kerr (2018),
among others). These papers extend the Klette and Kortum (2004) framework to include
het-erogeneity in innovation technologies in order to incorporate a more meaningful interaction
between different types of research (e.g., product versus process, radical versus incremental),
as well as between entrants and incumbent firms. These models are able to replicate the
observed size-dependence of growth and R&D through size-dependent R&D technological
ef-ficiency.8 In contrast, we propose a microfounded theory that is able to deliver size-dependent
growth and R&D intensity even in the absence of size-dependent R&D technologies. Our
novel trade-off between innovation and advertising decisions introduces the required
non-homogeneities in equilibrium. Specifically, we rely on two main strands of the marketing
literature in order to build a motive for advertising into our endogenous growth framework.
First, in our model, larger firms experience higher returns to advertising expenditures.
A large body of the marketing literature identifies this phenomenon as the equity value
of so-called “umbrella-branding”. These studies suggest that there exist spillovers between
goods within the firm, in the sense that increasing advertising expenditures on one good
not only increases sales for that good but also indirectly for all other goods under the same
brand. Lane and Jacobson (1995) and Tauber (1981, 1988) argue that brand developments
can decrease marketing costs, and Rangaswamyet al. (1993) suggest that they can enhance
marketing productivity. Moreover, Smith and Park (1992) show that they can help capture
greater market share. Morrin (1999) provides evidence that exposure to advertising of brand
extension facilitates parent brand recall. Using household scanner panel data for the U.S.,
Balachander and Ghose (2003) find a positive and significant spillover effect of advertising
for multiple product categories and geographic markets. Dacin and Smith (1994) show, by
means of controlled experiments, a positive relationship between the number of products
af-filiated with a brand and consumers’ confidence in the quality extension of the brand. Erdem
(1998) argues empirically that the quality perceptions of a brand in a product category are
positively affected by the consumer’s experience with the same brand in a different category,
because branding allows consumers to learn faster about quality through use experience.
More specifically for our purposes, Erdem and Sun (2002) show that the effects identified in
Erdem (1998) further translate to positive spillovers between advertising and sales for
differ-ent goods within the same brand. Particularly, such effects are presdiffer-ent in innovation-driven
industries, e.g. the car industry (Sullivan (1990) and B¨uschken (2007)) or the pharmaceutical
industry (see Suppliet (2016)).
The second observation that we draw from the marketing literature is that higher-quality
goods benefit relatively more from advertising: everything else equal, a good that compares
9See Kirmani and Rao (2000) and Bagwell (2007) for a survey of the literature.
sales per dollar spent into advertising. Archibald et al.(1983) and Caves and Greene (1996)
find a positive correlation between advertising and quality for innovative goods. Tellis and
Fornell (1988) examine the relationship over the product life cycle, and find that advertising
and profitability are both positively correlated to quality. Finally, Homer (1995), Kirmani
and Wright (1989) and Kirmani (1990, 1997) offer experimental evidence suggesting that
the positive relationship exists because consumers perceive higher advertising expenditures
indicating that the good is of high quality.9
Regarding advertising in Economics, our paper relates to a long tradition studying
ad-vertising as an explicit factor affecting consumer tastes, as in Dorfman and Steiner (1954),
Dixit and Norman (1978), Becker and Murphy (1993) and Benhabib and Bisin (2002). Our
approach is similar to those in that firms’ advertising effectively acts as a demand shifter in
equilibrium. A parallel body of literature introduces a role for valuable customer capital into
macro models, viewing marketing as a tool to build continuing buyer-seller relationships for
firms due to either the existence of frictions in product markets (e.g. Gourio and Rudanko
(2014b), Hall (2008), Roldan and Gilbukh (2018)) or because of costs to market penetration
(e.g. Arkolakis (2010, 2016) and Eaton et al. (2014)). Dinlersoz and Yorukoglu (2012) and
Perla (2017) view advertising as a way of signalling firm efficiency and raising product
aware-ness among customers, respectively, and focus on the implications for industry dynamics and
the degree of market competition. Fitzgerald and Priolo (2018) find empirical support for the
idea that marketing and advertising activities are important for firm growth. Fishman and
Rob (2003) study the implications of customer accumulation for firm size and R&D choices,
but they also do not focus on how marketing and innovation interact. To our knowledge, only
Grossmann (2008) has considered this potential interaction in a general equilibrium model.
However, while in that paper advertising and R&D are assumed to be direct complements,
we opt to be agnostic about the degree of complementarity between the two, and instead
dis-cipline their substitutability by matching directly firm-level cross-sectional data. In addition,
we incorporate firm heterogeneity which allows us to study the implications of advertising
for firm dynamics. Moreover, our policy analysis puts a special emphasis on how advertising
alters both the R&D-vs-advertising composition of firm investment on the intensive margin,
and the size distribution of firms on the extensive margin.
3
Empirical Findings
In this section, we present empirical results on firm growth, R&D and advertising
expen-ditures. Some of the coefficients that we obtain will then be used to calibrate the model that
is presented in Section 4 where we show that these facts can be explained as the result of an
optimal allocation of resources between R&D and advertising at the firm level.
Data We use annual data on U.S. listed companies from Compustat over the period 1980-2015. Firms reporting nonpositive sales or nonpositive employment are excluded from the
10Using different thresholds does not change the sign nor the significance of the coefficients.
11Table A.2 shows similar results for all four facts when size is measured by assets and employment. no advertising expenditures) firms. To exclude outliers, we ignore firms experiencing
year-on-year sales growth rates of more than 1,000%, as well as R&D-to-sales and advertising-to-sales
ratios of more than 100%.10 Moreover, we exclude mergers and acquisitions, and in order
to correct for a possible survival bias in the growth regressions, we make the conservative
assumption that exiting firms have a growth rate of –100% in their last period of operation.
Basic descriptive statistics of the resulting sample are reported in Table A.1 of Appendix D.
Empirical Facts and Relation to the Literature Our main focus is on the
regres-sion results for the four empirical facts that we presented in Figure 1. We use firm sales as
our baseline measure of firm size.11 All four regressions are of the form:
yij,t=α0+β1log(Salesij,t) +β2F irmAgeij,t+β3F inConstij,t+αj+αt+uij,t
for firm iin industry j in year t, whereαt controls for time fixed effects andαj controls
for industry fixed effects. The dependent variable is:
yij,t∈
ΔSalesij,t Salesij,t
,log
R&Dij,t Salesij,t
,log
Advij,t Salesij,t
,log
R&Dij,t Advij,t
for each of the four facts, respectively. To control for firm characteristics, we include firm
age, which we measure as the number of years elapsed since the firm first appeared in the
sample,12 and a measure of financial constraints, which is the difference between sales and
purchases of common and preferred stock as a share of firm sales.
In the results that follow, Facts #1 and #2 (related to firm growth and R&D intensity,
respectively) confirm results that have already been discussed in the literature. We then
introduce two new facts that relate to advertising and R&D (Facts #3 and #4). These new
facts highlight that firms of different sizes have different advertising intensities and that they
use R&D and advertising in different proportions.
Fact #1: Smaller innovative firms grow faster on average.
Column (1) in Table 1 shows that there exists a significant deviation from Gibrat’s law
among innovative firms in our sample. The results show that larger innovative firms tend
to experience lower growth rates in terms of sales. A 1% increase in sales translates into a
0.0325% decrease in sale growth.
12This measure of firm age in the Compustat database is standard and has been used among others by Shumway
(2001), Lubos and Veronesi (2003) and Fama and French (2004).
13Haltiwangeret al. (2013) argue, using data about the whole universe of firms in the U.S., that the observed
deviation from Gibrat’s law does not systematically hold when one controls for firm age. In column (2) of Table 1, we find that the significant deviation from Gibrat’s law still holds after controlling for firm age in our sample of innovative firms.
These results provide evidence that is similar to that reported in Akcigit (2009) and
Akcigit and Kerr (2018).13 The phenomenon has also been studied in the literature within
(1) (2) (3) (4) ΔSales
Sales log
R&D
Sales
logSalesAdv logRAdv&D log(Sales) -0.0325 -0.1035 -0.0317 -0.0719
(0.00288) (0.00892) (0.01000) (0.0120)
F irm Age -0.00441 0.00296 0.000688 0.00227 (0.000367) (0.00161) (0.00190) (0.00219)
F in. Const. 0.00270 0.00538 0.00745 -0.00207 (0.00172) (0.00304) (0.00432) (0.00498)
Time FE
Industry FE
Observations 24856 24856 24856 24856
R2 0.09 0.50 0.28 0.28
Notes: Compustat data (1980-2015). The sample is restricted to firms reporting strictly pos-itive sales, strictly pospos-itive employment, strictly pospos-itive R&D and advertising expenditures, with year-on-year sales growth less than 1,000%, and R&D-to-sales and advertising-to-sales ratios of less than 100%. Mergers and acquisitions have been excluded from the sample. Age is measured as the elapsed time since the first observation in the data. Our measure of financial constraints is sale minus purchases of common and preferred stock, divided by sales. Sales and advertising expenditures are in thousands of U.S.D. Standard errors are clustered by firm (in parentheses).
Table 1: Firm level regressions (Fact #1 - #4).
on stochastic (Markov) productivity shocks, can replicate the negative correlation between
firm size and firm growth. If the set of productivity shocks is finite and mean-reverting, larger
firms (i.e., firms with higher productivity) eventually face a limit to growth and experience
lower average growth rates. Jovanovic (1982), in contrast, proposes a model of learning in
which firms receive noisy signals about their productivity. In his model, younger firms are
more uncertain about their productivity and hence learn more than older firms, leading to
higher growth rates. The correlation between firm size and firm growth in such a setting thus
comes through an age effect and the positive correlation between age and size. Consequently,
in this type of models, the observed association between firm size and firm growth should
vanish as one controls for firm age.14 Yet, we find that the size effect is still significant after
controlling for age.
Cooley and Quadrini (2001) link the dependence of firm growth on size and age to financial
market frictions. In a model of firm dynamics similar to that of Hopenhayn (1992), Cooley
and Quadrini (2001) show that the interaction of persistent productivity shocks with costly
equity issuance and default generates a higher financial leverage for small and young firms and
qualitatively replicates the decreasing relationship between firm size, firm age and expected
growth.15 In column (1) of Table 1, we find that the deviation from constant growth holds
after controlling for financial constraints.16
14Clementi and Palazzo (2016) propose an extension of the Hopenhayn (1992) model with capital accumulation
in which, conditional on size, growth rates are on average decreasing in age.
15See also Clementi and Hopenhayn (2006). Itenberg (2015) links the high innovation intensity of small firms to
their extensive use of external equity financing. For a related approach, see Schmitz (2017).
g ( ) p p
17Acemoglu et al.(2018) also propose a model in which older and larger firms invest relatively less in R&D and
grow more slowly as a result, while Acemoglu et al.(2014) link innovation to the age of managers.
Fact #2: Smaller innovative firms have higher R&D intensity on average.
An emerging trend in the economic growth literature has investigated the departure from
constant growth across firm size by linking it to another cross-sectional empirical fact related
to firm size: the higher R&D intensity of smaller firms (see, for example, Akcigit (2009),
Acemoglu and Cao (2015), and Akcigit and Kerr (2018)). As larger firms invest relatively
less in innovation, they experience relatively lower growth rates.17
Column (2) in Table 1 shows that this pattern holds in our sample as well: larger firms
are less R&D intensive. The effect of age on R&D intensity is positive though not strongly
significant. A 1% increase in sales translates into a 0.1035% decrease in the R&D expenditure
to sales ratio.
In sum, smaller innovative firms grow relatively faster, and these firms spend relatively
more in R&D. While we are not the first ones to make these observations using Compustat
data (see, for instance, Akcigit (2009) and Itenberg (2015)), we show in addition that size
remains significant after controlling for age and financial constraint both in growth and R&D
intensity regressions, which suggests that explanations based on the firm’s product life-cycle
and financial constraints cannot entirely account for the deviation from Gibrat’s law observed
in the data. We propose an alternative explanation for this deviation based on the interaction
between R&D and advertising in firms’ optimal decisions. For this, we present two new facts
which are used to calibrate our model.
Fact #3: Smaller innovative firms have higher advertising intensity on average.
Column (3) in Table 1 shows that advertising intensity is decreasing in firm size: smaller
firms spend more in advertising per dollar of sales. Once again, this correlation remains
significant after controlling for age and financial constraints. We find that a 1% increase in
sales translates into a 0.0317% decrease in the advertising expenditure to sales ratio.
Fact #4: Smaller innovative firms have higher R&D to advertising ratios on average.
Finally, in column (4) of Table 1, we find that larger firms tend to use relatively more
advertising than R&D, as the ratio of R&D to advertising expenditure is significantly
de-creasing in size. In particular, a 1% increase in sales leads to a 0.0719% decrease in the R&D
to advertising expenditure ratio. This suggests that as innovative firms grow larger, they
tend to substitute R&D for advertising. We also find that the effect of age on the relative
use of R&D and advertising is not robustly significant.
Overall, these results suggest that the interaction between R&D and advertising can
potentially affect firm growth through a size effect, consistent with the advertising spillover
that our model captures. In addition, our calibrated model will deliver all four of these
4
An Endogenous Growth Model with Advertising
Inspired by the empirical findings of the previous section, we build a theory of advertising
into a model of endogenous growth. The basic structure follows the framework set up by
Klette and Kortum (2004), and specifically allows for heterogeneous innovations as in the
recent work by Akcigit and Kerr (2018). The advertising theory, on the other hand, is based
on empirical regularities that we take from the marketing literature. Our broader goal is to
illustrate a novel interplay between innovation and advertising, which critically shapes firms’
dynamic incentives for growth and growth in the economy as a whole.
4.1
Environment
Preferences Time is continuous, infinite, and indexed by t∈R+. The economy is
popu-lated by a measure-one of identical, infinitely-lived individuals with discount rate ρ > 0. A
representative household has preferences given by:
U =
+∞
0
e−ρtlnCt
dt (1)
whereCt is consumption of the single final good, whose price is normalized toPt= 1,∀t.
The household is endowed with one unit of time every instant, which is supplied inelastically
to the productive sector of the economy in the form of labor. The wage rate is denoted by
wt and is determined endogenously to clear the labor market. The household owns all the
firms in the economy and carries each period a stock of wealth At, equal to the total value
of corporate assets. Wealth earns an instantaneous and time-varying rate of return rt. The
flow budget constraint is ˙At=rtAt+wt−Ct for a given A0 ≥0.
Final Good Sector The final good is produced by a representative final good firm using a measure-one continuum of input varieties, indexed byj ∈[0,1], which are supplied by an
intermediate good sector. Technology is given by the Cobb-Douglas production function:
Yt= 1 1−β
1
0
qjtβy1jt−βdj
where β ∈ (0,1). yjt is the quantity of intermediate good j that is used at time t.
Quantities are weighted by the term qjt, which stands for the quality of the good that is
beingperceived by agents in the economy.
Product Qualities The total perceived qualityqjtof a certain goodjat timetis defined by:
qjt ≡qjt(1 +djt)
Total perceived quality includes two components. The first component, referred to as the
intrinsicquality of the product and denoted byqjt >0, stands for the currently leading-edge
18We borrow the nomenclature “intrinsic”, “extrinsic” and “perceived” from the marketing literature (e.g.,
Zei-thaml (1988)).
a process of technical innovation. In particular, it advances on a ladder, as in the models of
Grossman and Helpman (1991) and Aghion and Howitt (1992). This phenomenon is induced
by expenditures into R&D at the productive sector level. The second component in total
perceived quality is the so-called extrinsic quality of the product, given by φjt ≡ qjtdjt,
wheredjt ≥0 denotes advertising-induced quality.18 This component of total quality refers
to the part of total perceived quality of a good that is induced by the producer’s advertising
efforts on that specific product. Therefore, we may also refer to φjt as the effectiveness of
advertising productj in periodt.
This functional form implies that intrinsic (qj) and extrinsic (φj) quality are substitutes
at the good level, as they enter additively into total quality. However, note that we also allow
for a degree of complementarity coming from the fact thatφjt is itself an increasing function
of intrinsic quality,qj. Namely, advertising is effective in raising perceived quality only if the
good has nonzero intrinsic quality, and it is more effective the higher the intrinsic quality
of the good. This dual substitution and complementarity is consistent with the marketing
literature reviewed in Section 2. It will also allow us flexibility when calibrating the model,
as in equilibrium the two technologies may be substitutes or complements at the firm level,
depending on parameter values.19
In our model, advertising acts as a preference shifter. This follows Dixit and Norman
(1978), Becker and Murphy (1993), Benhabib and Bisin (2002) and Molinari and Turino
(2015), among others, who model advertising through product-specific taste parameters or
as an explicit argument in the utility function.20 In Appendix G.2, we present various
alternative ways to model advertising and show that, in all cases, advertising appears as a
demand shifter.
We further adopt the view that advertising ispersuasive, and not purelyinformative. By
this we mean that consumers cannot choose what information to be exposed to, but rather
behave according to the shifts in tastes induced by advertising, which they take as given.21
Yet, as we show in Appendix G.2.4, a version of our model in which advertising is informative
about the product’s quality would also feature the type of demand shift in equilibrium that
our baseline specification exhibits.
Finally, although we model advertising as a static component of firm profits, its choice
embodies a general-equilibrium effect that critically changes the dynamic incentives of
acquir-ing new product lines through R&D, and it thus has an indirect effect on firm and economic
growth. For completeness, in Appendix G.2.1, we introduce an extension with accumulation
of a stock of advertising (or so-called “goodwill” accumulation) over time, and show that this
would not affect the qualitative results that we obtain in our baseline model.
Production Sector At any instant, there is an endogenously determined setF (of mea-sure F > 0) of active incumbent producers operating in a monopolistically competitive
19See the comparative statics in Appendix F.
20In the baseline model, advertising appears in the final good sector’s production function. In Appendix G.2.2,
we show that a model in which advertising features in the utility function is isomorphic to our baseline model.
product market. Each goodj ∈[0,1] is produced by a single firmf ∈ F, and a single firm
may own multiple goods. A firm owns a product if it can produce it at a higher intrinsic
quality than any other firm. A firm f is summarized by the countable set of products for
which it has the leading-edge technology, denotedJf ⊆[0,1]. The number of active product
lines owned by firm f is n≡ |Jf| ∈ Z+. Finally, the product portfolio quality of firm f is
given byqf ≡ {qj :j∈ Jf} ∈Rn+.
Each good varietyjis produced with linear technology,yjt = ¯Qtljt, whereljtis labor input
and ¯Qt ≡
1
0 qjtdj is the average intrinsic quality in the economy. This linear formulation
implies that all good producers face the same marginal cost, wt/Q¯t. Moreover, by making
production scale with aggregate quality, we can ensure that output grows at the same rate
as productivity, which is necessary for the existence of a balanced growth path equilibrium.
4.2
Quality Improvements
Even though R&D-induced intrinsic quality innovations in the production sector are the
only engine of long run growth in the economy, firms can choose to advertise on their currently
owned product lines in order to increase demand through the extrinsic quality margin. In
this section, we introduce both of these quality enhancement margins.
Improving Intrinsic Quality (q) Firms can invest in R&D to either improve their own
product lines (so-called internal innovation) or to build upon the intrinsic quality of goods
that are currently produced by other incumbent monopolists (so-calledexternal innovation).
Firms expand or contract in the product space on the basis of these innovations.22
Particularly, to create a Poisson flow ratezj ≥0 of improving the intrinsic quality of its
own product j∈ Jf, a firmf must spend a cost of Rz(zj) units of the final good. This cost
function is assumed to be convex in the innovation rate and linear in quality, so that
Rz(zj) =χq jzjψ
where χ > 0 and ψ > 1. If successful, internal R&D improves intrinsic quality by a
factor of (1 +λI)>1, so that qj,t+Δt= (1 +λI)qjt if there is only one innovation within an
arbitrarily small time interval of size Δt >0. The fact that Rz increases with qj captures
that more advanced technologies face higher R&D costs.
External R&D is undertaken by incumbents and potential entrants. For simplicity,
ex-ternal R&D is assumed to be undirected, so that the successful innovator uniformly draws
a good from the set [0,1].23 Incumbents and entrants face, however, different innovation
technologies.
22Garcia-Macia et al. (2016) show that both internal and external innovations by incumbent firms contribute
significantly to aggregate growth. In our model, advertising affects the firm R&D-size relationship through external innovation intensity only. Our calibration delivers a share of growth coming from internal innovation that is in line with Garcia-Maciaet al.(2016).
23By the law of large numbers, this draws a good that is almost-surely not in the innovator’s current portfolio of
On the one hand, entrants (firms withn= 0) must incur an expenditure of
Re(xe) =νQx¯ e
units of the final good in order to generate a Poisson flow rate of xe for acquiring their
first product, where ν >0 is a constant parameter. We assume that there is a measure-one
mass of potential entrants, and determinexe by a free-entry condition.24
On the other hand, in order to create a flow Poisson rate of Xn, an incumbent firm with
n ≥ 1 product lines must incur an expenditure of Rx(Xn, n) units of the final good. In
particular, the cost function is assumed to be convex in the rate of innovation,Xn, such that
Rx(Xn, n) =χQX¯ nψnσ
where χ >0, ψ > 1, and σ ≤ 0. If successful, external R&D improves intrinsic quality
by a factor of (1 +λE) >1, so that qj,t+Δt = (1 +λE)qjt for a randomly selected product
line j∈[0,1], if there is only one innovation within an arbitrarily small time interval of size
Δt >0.
We define total R&D expenditure by a firm of size nchoosing innovation rates ({zj}, Xn)
by:
Rn≡
j∈J
Rz(zj) +Rx(Xn, n) (2)
Slightly abusing terminology, we say that there exist decreasing, constant, or increasing
returns to scale in R&D if an n-product firms finds it respectively more expensive, as
ex-pensive, or less expensive to grow through innovation by a given rate than n firms of one
product each.
On the one hand, as we shall see, the specification forRz ensures thatzj =z,∀j, because
both costs and benefits of internal innovations are linear in quality. This is equivalent as
internal R&D scaling proportionally with firm size, which we label as constant returns to
scale. Therefore, the degree of returns to scale in the R&D technology operates solely through
external innovations.
Absent our advertising margin, it is this degree of scalability which determines whether
the model can deliver the empirically observed deviations from Gibrat’s law. With constant
returns to scale in innovation costs (i.e,ψ+σ= 1), ex-ante technological advantages do not
exist with respect to differences in firm size. In other words, in a model without advertising,
external innovation investment would in this case scale up one-for-one with added product
lines. This naturally delivers a theoretical version of Gibrat’s law, as in the model of Klette
and Kortum (2004): firm growth is independent of firm size,n.
Because this specialization of the model is ill-suited to analyze why smaller firms are more
innovation-intensive in the data, subsequent work has relaxed the assumption of homogeneity
of degree one on the returns to innovation. Akcigit and Kerr (2018) extend the Klette and
Kortum (2004) framework to incorporate decreasing returns to external R&D (i.e,ψ+σ >1).
24In equilibrium,x
In contrast, we remain agnostic regarding the degree of returns to scale of R&D. In our
model with advertising, we are able to replicate empirical patterns in the data (e.g.,
devi-ations from Gibrat’s law, and decreasing R&D and advertising intensities across firm sizes)
when there exist constant, and even increasing, returns to scale in R&D. Our formulation
of advertising, which relies on empirical evidence from the marketing literature, delivers as
an equilibrium outcome that smaller firms are more concerned with innovation even when
technological advantages in innovation might not be particularly tailored toward them. This
is because those firms are the ones that marginally benefit the most in terms of increased
advertising efficiency from an increase in the size of their portfolio of products. This is a
novel explanation that highlights the potential effects of firms’ advertising on firm growth,
and it can have significant implications in terms of aggregate growth as well as policy as
discussed in Section 7.25
Improving Extrinsic Quality (φ) Besides building upon the intrinsic quality
com-ponent of their products, firms can undertake advertising expenditures in order to enhance
quality on the extrinsic dimension. Specifically, for a firm of size n≥ 1 with a portfolio of
intrinsic qualities q, we assume the following function for advertising effectiveness on good
j∈ Jf:
φj =θjmζjnη (3)
where mj is the expenditure into advertising good j, with (ζ, η) ∈ R2+, and θj is a
good- and firm-specific efficiency component, defined by θj ≡θQqjqQ¯1−ζ. The object Qq ≡
qj∈qq
1/α j
α
is a within-firm measure of aggregate intrinsic quality, and θ ≥ 0 is the
component of advertising efficiency that is constant across time, goods and firms.
Equation (3) embodies some of the main effects of advertising identified by the marketing
literature reviewed in Section 2 that are necessary within our framework to confirm the four
main empirical facts listed in Section 3.
First, everything else equal, the return to advertising a goodjis increasing in advertising
expenditures on that same good (mj), where the parameter ζ > 0 controls the elasticity of
advertising returns to advertising expenditure. To discipline this parameter, we rely on ample
evidence in Marketing establishing diminishing returns to advertising expenditures (Simon
and Arndt (1980), Sutton (1991), Jones (1995) and Bagwell (2007)), and thus assume that
ζ < 1. This concavity assumption in the advertising function is also standard in economic
models with marketing, e.g. Stigler (1961), Arkolakis (2010) and Dinlersoz and Yorukoglu
(2012).26
Second, the marketing return increases in the object qj/Qq, which is a measure of the
relative quality of the good within the firm. That is, advertising is more effective for goods
25In Appendix G.1, we extend our baseline model with a theory of patent citations following Akcigit and Kerr
(2018). Our model can deliver two other empirical regularities i.e. smaller firms tend to produce relatively more patents and those patents tend to be of higher quality.
26In addition, effectiveness is also concave in aggregate quality ¯Qto ensure the existence of a balanced growth
that are intrinsically of relatively higher quality compared to other products in the firm.
This implies that, in equilibrium, firms spend relatively more on advertising higher intrinsic
quality products, a result that has been identified empirically by the marketing literature
(e.g. Archibald et al. (1983), Caves and Greene (1996), Marquardt and McGann (1975),
Rotfeld and Rotzoll (1976), Bagwell (2007) and Kirmani and Rao (2000)).
Third, and critically for our mechanism, larger firms have an absolute marketing
advan-tage over smaller firms in that, everything else equal, the return to advertising is greater for
highern(η >0). We interpret this as there being spillover effects within the firm. This effect
is meant to capture the value of firm branding, as it is reminiscent of the “umbrella
brand-ing” effect discussed in the empirical marketing literature (e.g. Lane and Jacobson (1995),
Tauber (1981, 1988), Rangaswamy et al. (1993), Smith and Park (1992), Balachander and
Ghose (2003), Erdem (1998) and Erdem and Sun (2002)).
4.3
Entry and Exit, Pricing and Resource Constraints
There is no exogenous exit, and firms move endogenously on the size distribution in a
step-wise fashion via the external innovation margin. Creative destruction occurs whenever
a good is taken over by a successful external innovator, and a firm exits when it loses its last
remaining product.
We assume that a firm produces a good if it possesses a technological leadership on it.
The last innovator in each product line then owns the leading patent and has monopolistic
power until it is displaced by another firm. Once a firm makes an innovation, it acquires a
perpetual patent on it. However, this patent does not preclude other firms from investing into
research to improve the intrinsic quality of the product. As it is standard in the literature,
we assume that the new innovator is able to price the old incumbent out of the market and
charge the unconstrained monopoly price.
The economy is closed so GDP equals aggregate consumption plus aggregate investment.
The latter is split between aggregate R&D expenditure by entrants and incumbents,
de-noted Zt, and aggregate advertising expenditure by incumbents, denotedMt. The resource
constraint at time tis
Ct+Zt+Mt≤Yt (4)
Finally, the labor market must clear. Labor demand comes from intermediate goods
producers only, and therefore feasibility requires that01ljtdj≤1 for allt∈R+.
4.4
Equilibrium
In this section we derive the Markov Perfect Equilibrium of the economy. Later on, we
specialize the equilibrium to a balanced-growth path (BGP) in which all aggregates grow at
a constant and positive rate, g.
Consumer’s Problem Taking initial wealth A0 as given, the representative consumer
chooses a path for consumption to maximize utility subject to the flow budget constraint and
a no-Ponzi condition, limt→+∞e− t
0rsdsAt≥0. The optimality condition yields the standard
Euler equation for consumption:
˙ Ct Ct
=rt−ρ (5)
Intermediate-good firms are owned by the household, so the value of household wealth
is equal to the value of corporate assets. Namely, At =
FV(qf)df, where V(qf) denotes the net present value of the whole future expected stream of profits for a monopolist f who
owns the (intrinsic) quality portfolioqf at timet. In equilibrium, the following transversality
condition holds:
lim t→+∞
e−0trsds
FVt(qf)df
= 0 (6)
Final Good Firm’s Problem The representative final good producer takes qualities
{qj : j ∈ [0,1]} and input prices {pj : j ∈ [0,1]} as given and chooses intermediate goods
{yjt :j∈[0,1]}to maximize profits. This leads to:
pjt =
qjt yjt
β
(7)
Recalling that qjt =qjt(1 +djt), Equation (7) says that the inverse demand function for
goods is iso-elastic, and β is the price-elasticity. Importantly, this demand function makes
apparent that advertising, by increasing total quality (qjt = qjt+φjt) through its extrinsic
component (φjt =qjtdjt), effectively impacts consumer preferences, and works as a demand
shifter that alters consumption decisions.27
Incumbent Firm’s Problem A monopolist chooses labor, quantities, prices, R&D and
advertising expenditures over each good in its portfolio in order to maximize the present
discounted value of the total future stream of profits. Our set-up allows us to break this
problem into a static part, in which the firm sets price, quantity and advertising expenditures
over the goods that it currently owns, and a dynamic part, in which R&D decisions are made.
Before the R&D and advertising choices, the static maximization problem of monopolist
j∈[0,1] holding the patent for the leading-edge intrinsic quality of good j is:
π(qjt) = max yjt
pjtyjt−wtljt
s.t. yjt = ¯Qtljt and pjt =qjtβy− β jt
where π stands for operating profits before advertising and R&D expenditures. The
27In Appendix G.2.5, we present an extension of the model in which advertising also affect the price-elasticity of
demand.
optimality condition impliespjt =
1 1−β
wt
¯
Qt, meaning that all monopolists set the same price every period, or pjt =pt,∀j. This price is the optimal unconstrained monopoly solution: a
constant markup over the marginal cost. Using labor market clearing, 01ljtdj = 1, we can
find the market-clearing wage wt = (1−β)
¯
Qt+ ¯Φt
β ¯
Q1t−β, where ¯Φt ≡
1
0 φjtdj denotes
pt=
¯
Qt+ ¯Φt ¯ Qt
β
(8)
Aggregate output is:
Yt= 1−β
β
¯
Qt+ ¯Φt
β¯
Q1t−β (9)
and flow operating profits before advertising costs can be written as:
πjt = ˜πtq˜jt (10)
where
˜ πt=β
¯
Qt ¯ Qt+ ¯Φt
1−β
(11)
is the component of profits that is constant across goods. Equation (10) shows that any
difference in flow profits across goods must be due to differences in either intrinsic or extrinsic
quality, or both. Therefore, R&D and advertising represent two non-mutually exclusive ways
to increase profits. From Equation (11), we can notice that the profit of a firm is a decreasing
function of the overall investment in advertising in the economy through ¯Φt.
Advertising Choices Henceforth, we drop time subscripts unless otherwise needed.
When choosing advertising expenditures (mj), a firm of size n and portfolio of (intrinsic)
qualitiesq∈Rn+ solves the static problem:
πadv ≡ max
{mj:j∈J }
qj∈q
π(qj+φ(mj, n))−mj
(12)
s.t. φ(mj, n) =θ
qj
qj∈qq
1/α j
αQ¯1−ζmζjn η
where πadv denotes flow profits after the advertising decision. We make the assumption
that α = 1−ζ in order to reduce the dimensionality of the parameter space and be able
to find closed-form expressions.28 The optimality condition gives good-specific advertising
28Our results would not be qualitatively affected by the choice of a different value of α because the main
mechanism regarding advertising and R&D intensity works through firm size n. In addition, this assumption implies a positive relationship between advertising expenditure and quality at the product level but not at the firm level. This is in line with empirical results in Archibaldet al.(1983) who study this relationship at both the product and brand level. A similar result is obtained in Caves and Greene (1996) at the brand level.
expenditures of
and thus firm-level advertising expenditures of
Mn≡
qj∈qf mj =
ζθπ1−1ζQn¯ 1−ηζ (14)
mj =
ζθπ1−1ζ q
1/(1−ζ)
j
jq
1/(1−ζ)
j
¯
for a firm of sizen. Recall from our empirical analysis that (i) advertising expenditures
are increasing in size, and (ii) advertising intensity is decreasing in size (Fact #3). The first
observation is delivered directly by the fact that η > 0. Defining advertising intensity by
Mn/n, in order to satisfy the second requirement it must be thatMn is concave in n. This
leads to the following parametric restriction: 1−ηζ <1.
Because we imposed diminishing returns to advertising (ζ <1), the empirically-informed
parameter restriction directly implies that η < 1. Since this parameter controls for the
degree of size spillovers coming from advertising (recall Equation (3)), we obtain that, in
order to replicate the decreasing advertising intensity, the spillover effect from size must be
marginally stronger for smaller firms. Namely, the gain in advertising return for an
n-to-(n+ 1) transition is higher whennis smaller. As a consequence, smaller firms are relatively
more concerned with expanding to new product markets, and they choose a relatively higher
external innovation intensity in equilibrium.
In sum, the mechanism implies that the interaction between R&D and advertising can
generate a decreasing R&D intensity with firm size (Fact #2) and hence a deviation from
Gibrat’s law (Fact #1). Our model can then qualitatively generate Facts 1 to 3 even in the
presence of non-decreasing returns to scale in R&D.
Combining returns and costs, we have that the overall static profits of the firm are
πadv =πq j∈qqj
Intrinsic profits
+γQn¯ 1−ηζ
Extrinsic
profits
(15)
where γ ≡ π˜γ˜ −(θ˜πζ)1−1ζ is constant across goods and firms. Equation (15) is the
static value of firm-level flow operating profits net of advertising expenditures. It has two
components. The first one grows linearly with the aggregate intrinsic quality within the
firm, with a factor of proportionality that does not vary across firms (although it typically
may grow with the economy). The second one is invariant to the firm’s intrinsic quality
portfolio, but is increasing and concave in firm size. This component comes from investment
in advertising and the extrinsic margin of product quality. While the first term is standard in
models of endogenous firm growth with scalable returns, the second term is new and critically
alters the dynamic incentives to conduct research vis-`a-vis advertising in the way that we
have described above.
BGP Equilibrium Characterization A Balanced Growth Path equilibrium is defined as an equilibrium allocation in which aggregate variables grow at a constant rate, denoted by
g >0. To show the existence of such an equilibrium, we make use of the fact that
economy-wide extrinsic quality ¯Φ in fact grows at the same rate as that of aggregate intrinsic quality.
Formally, we have that ¯Φ = Φ∗Q¯ where Φ∗ is a constant, both across time and firms. Under this result, it is clear from Equation (9) that, if a BGP exists where output grows at the rate
g, then g = ˙¯Q/Q. Moreover, we can note from Equation (11) that ˜¯ π is time-invariant, and
therefore flow operating profits before advertising costs can be written asπjt =πq˜jt in BGP,
By construction, we can express total aggregate extrinsic quality on the BGP as ¯Φ =
+∞
n=1F μnΦn, where μn is the invariant share of size-n firms (which we derive explicitly below), such that μn ∈ [0,1] and n+=1∞μn = 1. Combining ¯Φ = Φ∗Q¯ with the formula for
¯
Φ and the equilibrium firm-level extrinsic quality, we then obtain that Φ∗ is the solution to the following expression:
Φ∗=θ1−1ζ
ζβ (1 + Φ∗)1−β
ζ
1−ζ +∞
n=1
F μnn η
1−ζ (16)
Equation (16) delivers a unique solution Φ∗ > 0. A direct consequence of the result is that aggregate marketing expenditures, M, grow at the rate g, since M = +n=1∞F μnMn, and Mn has been shown to be linear in ¯Q (Equation (14)). In particular, we obtain
M =
+∞
n=1
F μn
ζθπ1−1ζn1−ηζQ¯ (17)
and thus ˙M /M =g. From the resource constraint in (4), if total R&D expenditures Z
grow at the rate of ¯Q (a result whose proof we relegate to the end of this section), so does
aggregate consumption, C. From Equation (5), we then have thatg =rt−ρ, and therefore
rt=r=g+ρ,∀t.
Value Functions We now describe the R&D choices of firms. Denote byτthe endogenous
rate of creative destruction along the BGP, and byxnthe external R&D intensity of a firm of
sizen, i.e. xn ≡Xn/n, where Xn is the Poisson rate of external innovation. Taking (r, τ, g)
as given, a firm f with a product portfolio with 1≤n =|qf| goods chooses external R&D
intensity xn, and internal R&D intensities {zj : j ∈ Jf}, to maximize firm value Vn(qf),
written in the Hamilton-Jacobi-Bellman form (see Appendix A.1 for a derivation):
rVn(qf) = max xn,{zj}
qj∈qf
πqj−χz jψqj+zj
Vn
qf\−{qj} ∪+{qj(1 +λI)}
−Vn(qf)
+τ
Vn−1
qf\−{qj}
−Vn(qf)
+nxn
1
0
Vn+1
qf ∪+{qj(1 +λE)}
dj−Vn(qf)
−χnσ+ψxψQ¯+γQn¯ 1−ηζ
+ ˙Vn(qf) (18)
subject to Equation (3), where∪+ and \− are multiset union and difference operators.29 The first two terms in the first line of Equation (18) are good-specific intrinsic flow operating
profits net of internal R&D costs. The third term in the first line is the change in value due
to the internal improvement over a currently held good. This event occurs at a Poisson flow
rate ofzj, and it increases the intrinsic quality of the good by a factor of (1 +λI)>1. The
first term in the second line is the change in the firm’s value when losing a goodjto another
29These operators are defined by {a, b} ∪
+{b} = {a, b, b}, and {a, b, b}\−{b} = {a, b}, and they are needed
